Two-Dimensional Permutation Vectors’ (PV) Code for Optical

entropy

Article

Two-Dimensional Permutation Vectors’ (PV) Code forOptical Code Division Multiple Access Systems

Hassan Yousif Ahmed 1, Medien Zeghid 1,2 , Waqas A.Imtiaz 3 , Teena Sharma 4,* ,Abdellah Chehri 4,* and Paul Fortier 5

1 Electrical Engineering Department, College of Engineering at Wadi Aldwaseer, Prince Sattam Bin AbdulazizUniversity, Al-Kharj 16278, Saudi Arabia; [email protected] (H.Y.A.); [email protected] (M.Z.)

2 Electronics and Micro-Electronics Laboratory (E. µ. E. L), Faculty of Sciences, University of Monastir,Monastir 5000, Tunisia

3 Department of Electrical Engineering, Jalozai Campus, University of Engineering and Technology,Peshawar 23431, Pakistan; [email protected]

4 Department of Applied Sciences, University of Quebec in Chicoutimi (UQAC),Chicoutimi, QC G7H 2B1, Canada

5 Department of Electrical and Computer Engineering, Laval University, Québec, QC G1V 0A6, Canada;[email protected]

* Correspondence: [email protected] (T.S.); [email protected] (A.C.)

Received: 15 April 2020; Accepted: 16 May 2020; Published: 20 May 2020��

Abstract: In this paper, we present a new algorithm to generate two-dimensional (2D) permutationvectors’ (PV) code for incoherent optical code division multiple access (OCDMA) system to suppressmultiple access interference (MAI) and system complexity. The proposed code design approach isbased on wavelength-hopping time-spreading (WHTS) technique for code generation. All possiblecombinations of PV code sets were attained by employing all permutations of the vectors withrepetition of each vector weight (W) times. Further, 2D-PV code set was constructed by combiningtwo code sequences of the 1D-PV code. The transmitter-receiver architecture of 2D-PV code-basedWHTS OCDMA system is presented. Results indicated that the 2D-PV code provides increasedcardinality by eliminating phase-induced intensity noise (PIIN) effects and multiple user data canbe transmitted with minimum likelihood of interference. Simulation results validated the proposedsystem for an agreeable bit error rate (BER) of 10−9.

Keywords: OCDMA; vector permutation; phase induced intensity noise; multiple access interference;cross-correlation

1. Introduction

Driven by the ever-growing data size from internet usage rate, optical code division multipleaccess (OCDMA) system became the center of attention due to its ability to overcome the bottleneckproblem for data-hungry applications with massive data rate. OCDMA systems permit multiplesubscribers to asynchronously and concurrently access the medium without any contention along withthe ability to provide reliable bandwidth at relatively low cost [1,2].

Spectral amplitude coding (SAC) technique is measured as a proficient scheme in alleviating theeffects of multiple access interference (MAI) and its inherited intensity noise [3]. Along with its MAIalleviation features, SAC-OCDMA system is implemented with low cost and less complexity withbroadband incoherent sources such as light emitting diodes (LED) [4,5].

Two dimensional (2D) coding schemes are enthusiastically adapted to increase orthogonalitywhich lead to efficient bandwidth utilization. Further, performance is improved in terms of increasedsubscribers due to spectral density expansion at the cost of high-speed electronic devices [6].

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Entropy 2020, 22, 576 2 of 19

By combining two different dimensions of CDMA, two-dimensional (2D) codes have been proposedfor OCDMA networks. SAC-based systems mostly use spectral/spatial (S-S) and wavelength/time(W-T)-coding approaches for 2D coding [7,8]. In the case of 2D (W-T) scheme, a different wavelength isassigned to each chip and placed across the bit time period, which further offers higher transmissioncapacity and more flexibility when compared with 1D coding schemes [9–11]. Further, to improve biterror rate (BER) and cardinality for a certain data rate, AND detector circuit is used at the receiver [12].AND detector circuit composed of parallel structure of two photo detectors or photodiodes (PD ands-PD) which are connected electrically in opposition and power difference of the two optical inputs isthe resultant output signal.

The 2D W-T optical orthogonal codes (OOC) with constant weight and variable code lengthproperties were discussed by Yang et al. [13]. The 2D OOC code provides multimedia services withdistrict service requirements for optical CDMA networks by designing encoder and decoders withfiber bragg gratings (FBGs).

A new family of 2D hybrid W-T code was proposed by Kandouci et al. [14], by combining OCCand balanced incomplete block design zero cross-correlation (BIBD-ZCC) codes. The 2D hybridcode provides both off-peak auto-correlation and cross-correlation features with time-spreading andwavelength-hopping patterns. The presented code is suitable for the asynchronous and synchronousOCDMA environment with benefits such as high cardinality and good correlation properties.

The 2D W-T OCDMA system, which is based on coherent light sources, was analyzed in thepresence of beat noise (BN) and MAI effects by Bazan et al. [15]. For mitigating BN, a number ofaspects for 2D Time/Wavelength (TW) code designs are presented along with BN dependence oncode properties. Various 2D W-T codes based on single pulse per column/row and multiple pulse percolumn/row were compared. A new technique for designing OCDMA scheme with time spread andwavelength group hopping embedded maximum length (ML or m) sequence code was presented byChang et al. [16]. This technique uses cyclic and periodic free-spectral-range properties of arrayedwaveguide gratings (AWGs) routers to design 2D time-spreading and wavelength group-hoppingembedded m-sequence code. The code showed cross-correlation ((λc) = G ×w), where G stands fornumber of wavelengths and w referred as code weight. Fine AWG produces m-sequence code words,which is further time spread in the wavelength domain using a number of coarse AWGs.

Further, to design 2D zero cross-correlation (ZCC) code, W-T coding approach was used toobtain an increased number of subscribers by Kandauci et al. [17]. In this work, 2D ZCC codes weredesigned based on 1D ZCC codes while conserving same code length and correlation constraint.The proposed system architecture is simple and cost effective due to direct detection techniqueemployed at the receiver.

Multi-diagonal prime hop code (2D MDPHC) based on W-T coding technique and with zerocross-correlation properties was presented by Panda et al. [18]. The presented code is a combinationof two different 1D codes (MD and prime code) and can accommodate a larger number of userswith an increased data transmission rate. The entropy in information theory explains the disorder ofinformation. These types of imports are important and necessary because a well-developed identityin one discipline will bring definition to a phenomenon as well as mathematical tools and theory.Our aim here was to obtain crisp results in a simple setting which can be used to understand thebasic trade-offs between the intrinsic entropy rate of the system and the available rate on the opticalcommunication [19].

A passive optical network (PON) system based on 2D-OCDMA wavelength division multiplexing(WDM) was presented by Mrabet et al. [20] in which a hybrid of 2D prime hop system (PHS) codesand 2D hybrid coded (HC) signature codes were employed for uplink and WDM scheme for thedownlink. A vertical cavity surface emitting laser was deployed with an avalanche photo detectorreceiver and optical line terminal unit in the optical network. The system performance was analyzedfor the BER, signal to noise (SNR), optical power budget, and quality (Q) factor. BER improvement

Entropy 2020, 22, 576 3 of 19

(10−10 at data rates 40 Giga bits per second (Gbps)) as well as long PON distance up to 41 km withincreased maximum throughput equal to 285.1 Gb/s/km was achieved.

Moreover, Najjar et al. [21] proposed the construction of 2D diagonal eigenvalue unity (DEU)code using a spectral-spatial (S-S) coding approach with minimum cross-correlation. Results indicatedthat the 2D DEU provides an increase in cardinality when compared to existing 2D diluted perfectdifference DPD and 1D DEU codes.

Mrabet et al. [22] presented an analytical model consisting of a hybrid of all-optical orthogonalfrequency division multiplexing (AO-OFDM) and OCDMA. The presented model incorporatedprobabilistic subcarrier overlapping and MAI testing capabilities with over amplifier-free long-reachpassive optical networks (LR-PONs) using cost-effective intensity modulations and direct detection(IM-DD) techniques. The proposed system considered subcarrier hopping by utilizing 2D-HC codes.It was observed that the hybrid (AO-OFDM) and OCDMA with 2D-HC outperformed a traditionalmultichannel OCDMA system for any number of simultaneous users and low received powersin comparison with 1D-Walsh Hadamard, 1D, and 2D prime codes. Numerical results showedthat 16-quadrature amplitude modulation (16-QAM) AO-OFDM-OCDMA provides comparableperformance to traditional multichannel 16-QAM coherent optical OFDM in the downstream direction.The presented technique supported up to 58 km with a maximum 45 users, without complex coherenttechnology. In addition, at 108 km as a maximum reachable distance (at 40 Gb/s), QAM signalwas achieved in budget power calculation while considering standard forward error correction(FEC) techniques.

Further, a recent study conducted by Mrabet et al. [23] presented performance analysis of anOCDMA system for LR-PON systems, considering MAI, receiver noise, and single-mode fiber (SMF)channel effects. A mathematical model representing 2D optical code parameters for different receiverstructures using Matlab simulations was developed including effects of channel imperfections, such asattenuation losses and chromatic dispersion. Probability of error was investigated for back-to-back (B2B)single mode fiber (SMF) with conventional correlation receiver (CCR) and SMF channel with successiveinterference cancelation (SIC) receiver. Performance improvement, in terms of number of simultaneoususers with Q factor (6) at fiber distances 190 and 120 km, was achieved without amplification.

The rest of this manuscript is arranged as follows. Section 2 describes the construction andproperties of the 2D wavelength/time permutation vectors’ codes. Section 3 presents the architectureof the transmitter and receiver of the proposed code. Section 4 analyzes the system performance.The numerical and simulation results are presented in Sections 5 and 6, respectively. Finally, theconclusions are drawn in Section 7.

2. The 2D Wavelength-Hopping/Time-Spreading System

Utilizing a wavelength-hopping/time-spreading (WHTS) as encoding technique for 2Drepresentation provides numerous advantages over other incoherent schemes such as cardinality andcode interference mitigation. In this approach, the codes were spread in both the time and wavelengthdomains simultaneously.

Three different cases were demonstrated to represent the wavelength-time slots matrices inFigure 1. Firstly symmetric case (SC) is shown in Figure 1a, in which all assigned wavelengths wereutilized and every wavelength appeared only once in each code sequence at different time slots.Secondly, asymmetric case (AS) occurred if at least two different wavelengths were located at the sametime slot or if the same wavelength appeared twice or more at different time slots (Figure 1b,c).

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Figure 1. Classification of 2D W-T PV codes (a) (λ1 λ3 0 λ2 0 λ4) (b) ({λ1, λ4} 0 0 λ2 0 λ4) (c) (λ1 0 λ3 0 λ3 0 λ2). *λ=Wavelength

3. The 2-dimensional wavelength-time (W-T) Permutation Vectors’ (PV) Code Construction and Properties

The new 1D PV code was constructed based on permutation vectors. It is characterized by the code length (L), the code weight (w), and by zero cross-correlation. L depends on the number of users (K) and w. The relationship of these variables is given as follows: 𝐿 = 𝑤𝐾. (1)

3.1. One-Dimensional Approach

Let ℝ refer to the field of real numbers. The space of all m-tuples of real numbers forms an m-dimensional vector space over ℝ and represented by ℝ . The dimension of the vector space U over the field ℝ can be written as dim ℝ (U) or as [U: ℝ]. An element U of ℝ can be represented as vertical vector:

𝑈 = ⎩⎪⎨⎪⎧ 𝑢𝑢..𝑢 ⎭⎪⎬

⎪⎫. (2)

Therefore, the dim ℝ(ℝ3) = 3. In general, dimℝ(ℝm) = m.

Using the standard unit basis vectors, any vector 𝑈 = ⎝⎜⎛ 𝑢𝑢..𝑢 ⎠⎟

⎞ ∈ ℝ can be expressed as a linear

combination 𝑈 = 𝑢 𝑒 𝑢 𝑒 ⋯ 𝑢 𝑒 , where 𝑒 , 𝑒 , … , 𝑒 are the standard unit basis vectors of ℝm.

Let T: ℝ → ℝ be a linear transformation defined such that:

𝑇(𝑒 ) = ⎝⎜⎜⎛100..0⎠⎟⎟

⎞ ; 𝑇(𝑒 ) = ⎝⎜⎜⎛010..0⎠⎟⎟

⎞ ; … … , 𝑇(𝑒 ) = ⎝⎜⎜⎛000..1⎠⎟⎟

⎞. (3)

The representation matrix is:

[𝑇(𝑒 ), 𝑇(𝑒 ), … , 𝑇(𝑒 )] =⎝⎜⎜⎜⎛⎝⎜⎜

⎛100..0⎠⎟⎟⎞ ; ⎝⎜⎜

⎛010..0⎠⎟⎟⎞ ; … . ; ⎝⎜⎜

⎛000..1⎠⎟⎟⎞

⎠⎟⎟⎟⎞, (4)

For example, the vector space ℝ4 is represented as:

Figure 1. Classification of 2D W-T PV codes (a) (λ1 λ3 0 λ2 0 λ4) (b) ({λ1, λ4} 0 0 λ2 0 λ4) (c) (λ1 0 λ3 0 λ3

0 λ2). * λ = Wavelength.

3. The 2-Dimensional Wavelength-Time (W-T) Permutation Vectors’ (PV) Code Constructionand Properties

The new 1D PV code was constructed based on permutation vectors. It is characterized by thecode length (L), the code weight (w), and by zero cross-correlation. L depends on the number of users(K) and w. The relationship of these variables is given as follows:

L = wK. (1)

3.1. One-Dimensional Approach

Let R refer to the field of real numbers. The space of all m-tuples of real numbers forms anm-dimensional vector space over R and represented by Rm. The dimension of the vector space Uover the field R can be written as dim R (U) or as [U: R]. An element U of Rm can be represented asvertical vector:

U =

u1

u2

.

.um

. (2)

Therefore, the dim R(R3) = 3. In general, dim R(Rm) = m.

Using the standard unit basis vectors, any vector U =

u1

u2

.

.um

∈ Rm can be expressed as a linear

combination U = u1e1 + u2em + . . .+ umem, where e1, e2, . . . , em are the standard unit basis vectorsof Rm.

Let T: Rm→ Rm be a linear transformation defined such that:

T(e1) =

100..0

; T(e2) =

010..0

; . . . . . . , T(em) =

000..1

. (3)

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The representation matrix is:

[T(e1), T(e2), . . . , T(em)] =

100..0

;

010..0

; . . . .;

000..1

, (4)

For example, the vector space R4 is represented as:

[T(e1), T(e2), T(e3), T(e4)] =

1000

;

0100

;

0010

;

0001

A permutation vector is a 1 × n or n × 1 vector of the integers 1 through n. The followingpermutation matrix and permutation vector are equivalent:

Perm =

1234

⇔ [T(e1), T(e2), T(e3), T(e4)] =

1000

;

0100

;

0010

;

0001

Based on the above definitions and given the number of users K and the weight W, we cangenerate all possibilities of 1D-PV by getting all permutations of the vectors with repetition of[T(e1), T(e2), . . . , T(ek−1)] each vector w times. Hence, the 1D-PV codes consists of K × l matrixfunctionally depending on the value of the number of users (K) and code weight (w). These 1D-PVcodes were constructed based on the vector space Rk and an arbitrary permutation vector (Perm).

1D− PV =(Rk

∣∣∣Perm)k×l

, (5)

where Perm is a permutation vector used to permute the columns of the representation matrix of Rk,the permuted Rk is obtained using Equation (6):

Rk = Rk[., Perm]. (6)

Moreover, the proposed 1D− PV is designed such that:

• Cross-correlation between each row is equal to 0.• Each column is an element of the vector space Rk.

• Number of Perm possibilities is equal to PVposs =(WK)!

(w!(L−w)!) .

Thus, the basic form of 1D− PV for k = w = 2 while using the above-mentioned properties can bewritten in six forms as:

(1D− PV)1 =(R2

∣∣∣(1, 1, 2, 2))= [T(e1), T(e1), T(e2), T(e2)] =

(1 1 0 00 0 1 1

)

(1D− PV)2 =(R2

∣∣∣(1, 2, 1, 2))= [T(e1), T(e2), T(e1), T(e2)] =

(1 0 1 00 1 0 1

)

(1D− PV)3 =(R2

∣∣∣(1, 2, 2, 1))= [T(e1), T(e2), T(e2), T(e1)] =

(1 0 0 10 1 1 0

)

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(1D− PV)4 =(R2

∣∣∣(2, 2, 1, 1))= [T(e2), T(e2), T(e1), T(e1)] =

(0 0 1 11 1 0 0

)

(1D− PV)5 =(R2

∣∣∣(2, 1, 2, 1))= [T(e2), T(e1), T(e2), T(e1)] =

(0 1 0 11 0 1 0

)

(1D− PV)6 =(R2

∣∣∣(2, 1, 1, 2))= [T(e2), T(e1), T(e1), T(e2)] =

(0 1 1 01 0 0 1

)An example of PV codes generated with weight w = 2 and K = 4 are given in Table 1. The number

of possibilities is 28 sets of different patterns of PV code as a product of permutation operation.

3.2. W-T Two-Dimensional PV Approach

The obtained 2D W-T OCDMA codes were generated either by using a mathematical approachor by extension of an existing one-dimensional code. In the proposed work, 2D W-T PV codes wereobtained by using one-dimensional PV codes for both wavelength-hopping and time-spreading. Thenew codes can be constructed as follows.

First, we construct M groups of PV codes as follows where M is ranging between 1 and PVposs.

PV = {G1, G2, G3, . . . . . . .GM}, (7)

where Gi is 1D-PV code constructed based on the vector space R k and an arbitrary permutation vector(Permi), so that:

Entropy 2020, 22, x FOR PEER REVIEW 6 of 20

An example of PV codes generated with weight w = 2 and K = 4 are given in Table 1. The number of possibilities is 28 sets of different patterns of PV code as a product of permutation operation.


The obtained 2D W-T OCDMA codes were generated either by using a mathematical approach or by extension of an existing one-dimensional code. In the proposed work, 2D W-T PV codes were obtained by using one-dimensional PV codes for both wavelength-hopping and time-spreading. The new codes can be constructed as follows.

First, we construct M groups of PV codes as follows where M is ranging between 1 and 𝑃𝑉 . 𝑃𝑉 = 𝐺 , 𝐺 , 𝐺 , … … . 𝐺 , (7) where 𝐺 is 1D-PV code constructed based on the vector space ℝk and an arbitrary permutation vector (𝑃𝑒𝑟𝑚𝑖), so that: 𝐺 𝐺 𝐺 𝐺 …………...... 𝐺 𝟎𝟎𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟏𝟎𝟎𝟎𝟎

𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟏𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎

00010001100010000100001000100100

01001000000100100010000110000100

…………...... …………….. …………….. ……………...

00100100010000100001000110001000

𝐺 𝐺 𝐺 …………….. 𝐺 𝟎𝟎𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟏𝟎𝟎𝟎𝟎

𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟏𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎

00010001100010000100001000100100

01001000000100100010000110000100

…………….. …………….. …………….. ……………...

00100100010000100001000110001000

𝐺 = ℝ [. , 𝑃𝑒𝑟𝑚𝑖] = 𝐶 , 𝐶 , 𝐶 , … … . 𝐶 , where, 𝐶 is a 1D-PV code where 𝑖 ∈ [1, 𝑀] and 𝑗 ∈ [1, 𝐾] and K is the number of generated codes in the group. Hence 𝐶 is an arbitrary code in 𝐺 . The 2D W-T PV codes can be constructed by selecting 𝐺 to generate L time slots. Each 𝐶 will be used as time-spreading patterns to determine the positions of the wavelengths. For the wavelength-hopping patterns, another 1D-PV code group was used 𝐺 , where d ≠ i. Hence, the wavelength-hopping patterns form the wavelength’s index. Between two selected groups (Gi and Gd), the total number of served users = K2. Therefore, the 2D W-T PV codes’ generation equation was defined as: 𝐴 , = 𝐺 𝐺 = 𝐶 𝐶 ⋯ 𝐶 𝐶⋮ ⋱ ⋮𝐶 𝐶 ⋯ 𝐶 𝐶 . (8)

Table 1. 1-dimensional-PV codes generated with code weight (w) = 2 and number of generated codes (K) = 4.

Each element in 𝐴 , is a square matrix (L× L), where L represents the number of available wavelengths and the number of time slots. The 2D W-T PV codes matrices were obtained by associating the rows with wavelengths and the columns with time slots. For example, choose i = 1 and d = 2 (group 1 and group 2 from Table 1). Then the code matrix 𝐶 𝐶 is represented as follows.

Gi = Rk1[., Permi] = {Ci1, Ci2, Ci3, . . . . . . .Cik},

where, Ci j is a 1D-PV code where i ∈ [1, M] and j ∈ [1, K] and K is the number of generated codes inthe group. Hence Ci j is an arbitrary code in Gi. The 2D W-T PV codes can be constructed by selectingGi to generate L time slots. Each Ci j will be used as time-spreading patterns to determine the positionsof the wavelengths. For the wavelength-hopping patterns, another 1D-PV code group was used Gd,where d , i. Hence, the wavelength-hopping patterns form the wavelength’s index. Between twoselected groups (Gi and Gd), the total number of served users = K2. Therefore, the 2D W-T PV codes’generation equation was defined as:

Ad,i = GTd Gi =

Cd1Ci1 · · · Cd1Cik

.... . .

...CdkCi1 · · · CdkCik

. (8)

Entropy 2020, 22, 576 7 of 19

Table 1. 1-dimensional-PV codes generated with code weight (w) = 2 and number of generated codes(K) = 4.


An example of PV codes generated with weight w = 2 and K = 4 are given in Table 1. The number of possibilities is 28 sets of different patterns of PV code as a product of permutation operation.


The obtained 2D W-T OCDMA codes were generated either by using a mathematical approach or by extension of an existing one-dimensional code. In the proposed work, 2D W-T PV codes were obtained by using one-dimensional PV codes for both wavelength-hopping and time-spreading. The new codes can be constructed as follows.

First, we construct M groups of PV codes as follows where M is ranging between 1 and 𝑃𝑉 . 𝑃𝑉 = 𝐺 , 𝐺 , 𝐺 , … … . 𝐺 , (7) where 𝐺 is 1D-PV code constructed based on the vector space ℝk and an arbitrary permutation vector (𝑃𝑒𝑟𝑚𝑖), so that: 𝐺 𝐺 𝐺 𝐺 …………...... 𝐺 𝟎𝟎𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟏𝟎𝟎𝟎𝟎

𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟏𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎

00010001100010000100001000100100

01001000000100100010000110000100

…………...... …………….. …………….. ……………...

00100100010000100001000110001000

𝐺 𝐺 𝐺 …………….. 𝐺 𝟎𝟎𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟏𝟎𝟎𝟏𝟎𝟎𝟎𝟎

𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟏𝟏𝟎𝟎𝟎𝟎𝟎𝟏𝟎𝟎𝟏𝟎𝟏𝟎𝟎𝟎𝟎

00010001100010000100001000100100

01001000000100100010000110000100

…………….. …………….. …………….. ……………...

00100100010000100001000110001000

𝐺 = ℝ [. , 𝑃𝑒𝑟𝑚𝑖] = 𝐶 , 𝐶 , 𝐶 , … … . 𝐶 , where, 𝐶 is a 1D-PV code where 𝑖 ∈ [1, 𝑀] and 𝑗 ∈ [1, 𝐾] and K is the number of generated codes in the group. Hence 𝐶 is an arbitrary code in 𝐺 . The 2D W-T PV codes can be constructed by selecting 𝐺 to generate L time slots. Each 𝐶 will be used as time-spreading patterns to determine the positions of the wavelengths. For the wavelength-hopping patterns, another 1D-PV code group was used 𝐺 , where d ≠ i. Hence, the wavelength-hopping patterns form the wavelength’s index. Between two selected groups (Gi and Gd), the total number of served users = K2. Therefore, the 2D W-T PV codes’ generation equation was defined as: 𝐴 , = 𝐺 𝐺 = 𝐶 𝐶 ⋯ 𝐶 𝐶⋮ ⋱ ⋮𝐶 𝐶 ⋯ 𝐶 𝐶 . (8)

Table 1. 1-dimensional-PV codes generated with code weight (w) = 2 and number of generated codes (K) = 4.

Each element in 𝐴 , is a square matrix (L× L), where L represents the number of available wavelengths and the number of time slots. The 2D W-T PV codes matrices were obtained by associating the rows with wavelengths and the columns with time slots. For example, choose i = 1 and d = 2 (group 1 and group 2 from Table 1). Then the code matrix 𝐶 𝐶 is represented as follows.

Each element in Ad,i is a square matrix (L × L), where L represents the number of availablewavelengths and the number of time slots. The 2D W-T PV codes matrices were obtained by associatingthe rows with wavelengths and the columns with time slots. For example, choose i = 1 and d = 2(group 1 and group 2 from Table 1). Then the code matrix C21C11 is represented as follows.Entropy 2020, 22, x FOR PEER REVIEW 7 of 20

퐶 퐶 =

⎝

⎜⎜⎜⎛

0 0 00 0 0000000

000000

000100

0 0 0 0 00 0 0 0 0000000

000000

000000

010000

000000⎠

⎟⎟⎟⎞

’ ×

As shown in Figures 2 and 3, the 2D W-T PV generated codes were differentiated with either the wavelength’s hopping or the time spreading.

Figure 2. Code’s illustration C C , C C , and C C .

For example, from Figure 2, it is clear that the codes 퐶 퐶 (pink colored) and 퐶 퐶 (blue colored) shared the same spectral signature (λ3, λ5) but transmitted them at different time slots (t3, t7) and (t5,t6), respectively. Furthermore, when two codes used the same time slots, like 퐶 퐶 and 퐶 퐶 (green colored), they sent different wavelengths, (λ3, λ5) for 퐶 퐶 and (λ6, λ8) for 퐶 퐶 , thus maintaining a zero cross-correlation.

Figure 3. A 3-dimensional (3D) graphic representation of 2D W-T PV code sequences.

Figure 3 shows a 3-dimensional (3D) graphic representation of two 2D W-T PV code sequences, which represent either time spreading or wavelength hopping. It is clear that user#5 and user#6 shared the same spectral signature with spreading at different time slots.

As shown in Figures 2 and 3, the 2D W-T PV generated codes were differentiated with either thewavelength’s hopping or the time spreading.


𝐶 𝐶 =⎝⎜⎜⎜⎛

0 0 00 0 0000000000000

000100

0 0 0 0 00 0 0 0 0000000000000

000000010000

000000⎠⎟⎟⎟⎞

’ ×



For example, from Figure 2, it is clear that the codes 𝐶 𝐶 (pink colored) and 𝐶 𝐶 (blue colored) shared the same spectral signature (λ3, λ5) but transmitted them at different time slots (t3, t7) and (t5,t6), respectively. Furthermore, when two codes used the same time slots, like 𝐶 𝐶 and 𝐶 𝐶 (green colored), they sent different wavelengths, (λ3, λ5) for 𝐶 𝐶 and (λ6, λ8) for 𝐶 𝐶 , thus maintaining a zero cross-correlation.



Figure 2. Code’s illustration C21C11, C21C12, and C22C12.

For example, from Figure 2, it is clear that the codes C21C11 (pink colored) and C21C12 (bluecolored) shared the same spectral signature (λ3, λ5) but transmitted them at different time slots (t3,t7) and (t5,t6), respectively. Furthermore, when two codes used the same time slots, like C21C12 andC22C12 (green colored), they sent different wavelengths, (λ3, λ5) for C21C12 and (λ6, λ8) for C22C12, thusmaintaining a zero cross-correlation.

Figure 3 shows a 3-dimensional (3D) graphic representation of two 2D W-T PV code sequences,which represent either time spreading or wavelength hopping. It is clear that user#5 and user#6 sharedthe same spectral signature with spreading at different time slots.

Entropy 2020, 22, 576 8 of 19


𝐶 𝐶 =⎝⎜⎜⎜⎛

0 0 00 0 0000000000000

000100

0 0 0 0 00 0 0 0 0000000000000

000000010000

000000⎠⎟⎟⎟⎞

’ ×



For example, from Figure 2, it is clear that the codes 𝐶 𝐶 (pink colored) and 𝐶 𝐶 (blue colored) shared the same spectral signature (λ3, λ5) but transmitted them at different time slots (t3, t7) and (t5,t6), respectively. Furthermore, when two codes used the same time slots, like 𝐶 𝐶 and 𝐶 𝐶 (green colored), they sent different wavelengths, (λ3, λ5) for 𝐶 𝐶 and (λ6, λ8) for 𝐶 𝐶 , thus maintaining a zero cross-correlation.




3.3. Properties of 2D W-T Permutation Vectors (PV) Codes

In order to define the cross-correlation of a 2D W-T PV code, four matrices are defined asEquations (10)–(13).

Ag,h(0) = Gh

T Gg (9)

Ag,h(1) = Gh

TGg (10)

Ag,h(2) = Gh

TGg (11)

Ag,h(3) = Gh

TGg. (12)

The cross-correlation between any arbitrary code, Ad,i, and characteristic code, Ag,h, can be definedthrough Equation (14).

Rpg,h(d, i) =

L−1∑f=0

L−1∑j=0

a(d,i)( f , j)a(p)(g,h)

( f , j), (13)

where a(p)(g,h)

and a(d,i) represent the elements of Ag,h(p) and Ad,i 2D W-T PV matrix, respectively,

and p ∈ [0, . . . , 3]. In accordance with Equation (11), the cross-correlation between any two codes Ag,hand Ad,i can be calculated as shown in Table 2.

Table 2. Cross-correlation values of 2D W-T PV codes.

R0g,h(d, i) R1

g,h(d, i) R2g,h(d, i) R3

g,h(d, i)

d = g, i = h w 0 0 0d = g, i , h 0 w 0 0d , g, i = h 0 0 w 0d , g, i , h 0 0 0 w

As the cross-correlation along Gi and GTd code sequences equals zero, so R(1,3)

g,h (d, i) has no use forthe new correlation function, which makes the multiple user interference (MUI) elimination processeasier. Hence, the expression of a new cross-correlation function from the previous table is givenas follows:

Rpg,h(d, i) =

{w, f or d = g, i = h0 otherwise

. (14)

Entropy 2020, 22, 576 9 of 19

4. 2-Dimensional PV System Description

4.1. Design of 2D-PV System

The basic 2D-PV-based OCDMA system comprises numerous W-T encoders/decoders at thetransmitter and receiver parts, respectively. Each encoder/decoder structure is made up of FBG-baseddelay lines, each with a certain bit period. FBGs as delay lines are preferred due to low circuitcomplexity and reduced delay time when compared to first generation 2D TW implementations(tunable filters and delay lines) [24]. Due to recent advancement in thin film technology, thin filmfilters (TFFs) are other alternative implementation approaches [25].

4.2. Design of 2D-PV Transmitter Part

The conventional transmitter structure for a W-T OCDMA system is shown in Figure 4. Initially,the transmitter module consists of a multi-wavelength continuous wave (CW) laser array as an opticalsource. For each user, a group of wavelengths is produced by the CW laser. These short pulse trainsare set to a width τ ((τ = tb/S), which represents code length in time spread), where tb/S stands forbit time period per second. The pulse train repetition rate is set equal to the system bit rate (1/tb).The bit stream is modulated by the input data using an amplitude modulator. In the on-off keyingprocess, the modulator produces an optical pulse when transmitted data bit is one, or else it produceszero output.


Modulated signal/data pulses are demultiplexed using a demultiplexer. Pulses corresponding to data bit one are sent to a 2D W-T-based optical encoder to perform encoding operation. The W-T encoder circuit is made up of time delay circuits and Bessel optical filters. In 2D TW codes, chosen pulses are encoded by different or similar spectral components according to the PV code algorithm (Table 1). Each optical pulse corresponding to transmitted bits is divided into w optical pulses with time delay (t) between each one of them. Finally, an encoded data stream (wavelength time-spreading patterns) is transmitted to a single-mode optical fiber through a power combiner.

Figure 4. Transmitter structure for 2D W-T PV optical code division multiple access system.

4.3. Design of 2D-PV Receiver Part

The receiver structure for a conventional 2D W-T OCDMA system is shown in Figure 5. The fiber output data is demultiplexed and sent to a 2D PV decoder circuit, which consists of low-pass Bessel filters and inverse time delay circuitry. Direct detection with a single-photo diode detector or balance detection technique can be employed for signal detection with a certain threshold level set to achieve the desired output. Finally, at the receiver, both input and output data are compared by BER test set and, therefore, BER analysis is carried out by BER test set. A Spectrum analyzer and optical time domain analyzer (OTDA) are used to analyze the changes in signal power and to measure spectrum of various signals with time at different points of the system.

Figure 5. Receiver structure for 2D-PV OCDMA system.

5. Proposed 2D-PV W-T-Based OCDMA-PON


Modulated signal/data pulses are demultiplexed using a demultiplexer. Pulses correspondingto data bit one are sent to a 2D W-T-based optical encoder to perform encoding operation. The W-Tencoder circuit is made up of time delay circuits and Bessel optical filters. In 2D TW codes, chosenpulses are encoded by different or similar spectral components according to the PV code algorithm(Table 1). Each optical pulse corresponding to transmitted bits is divided into w optical pulses withtime delay (t) between each one of them. Finally, an encoded data stream (wavelength time-spreadingpatterns) is transmitted to a single-mode optical fiber through a power combiner.


The receiver structure for a conventional 2D W-T OCDMA system is shown in Figure 5. The fiberoutput data is demultiplexed and sent to a 2D PV decoder circuit, which consists of low-pass Bessel

Entropy 2020, 22, 576 10 of 19

filters and inverse time delay circuitry. Direct detection with a single-photo diode detector or balancedetection technique can be employed for signal detection with a certain threshold level set to achievethe desired output. Finally, at the receiver, both input and output data are compared by BER test setand, therefore, BER analysis is carried out by BER test set. A Spectrum analyzer and optical timedomain analyzer (OTDA) are used to analyze the changes in signal power and to measure spectrum ofvarious signals with time at different points of the system.


Modulated signal/data pulses are demultiplexed using a demultiplexer. Pulses corresponding to data bit one are sent to a 2D W-T-based optical encoder to perform encoding operation. The W-T encoder circuit is made up of time delay circuits and Bessel optical filters. In 2D TW codes, chosen pulses are encoded by different or similar spectral components according to the PV code algorithm (Table 1). Each optical pulse corresponding to transmitted bits is divided into w optical pulses with time delay (t) between each one of them. Finally, an encoded data stream (wavelength time-spreading patterns) is transmitted to a single-mode optical fiber through a power combiner.



The receiver structure for a conventional 2D W-T OCDMA system is shown in Figure 5. The fiber output data is demultiplexed and sent to a 2D PV decoder circuit, which consists of low-pass Bessel filters and inverse time delay circuitry. Direct detection with a single-photo diode detector or balance detection technique can be employed for signal detection with a certain threshold level set to achieve the desired output. Finally, at the receiver, both input and output data are compared by BER test set and, therefore, BER analysis is carried out by BER test set. A Spectrum analyzer and optical time domain analyzer (OTDA) are used to analyze the changes in signal power and to measure spectrum of various signals with time at different points of the system.





Figure 6 shows the proposed architecture that incorporates a maximum of K1 ×K2 transmitters,N2 remote nodes, and K1 × K2 receiver modules. Here, K1 and K2 represent the number of spectraland temporal code word, whereas N2 is the temporal code length. Each subscriber is assigned with apart of the transmitter and receiver module corresponding to a 2D vector permutation code word Ag,h.Furthermore, a hybrid ring and tree-based topology is adapted at the feeder and distribution level tofacilitate deployment of the proposed architecture as a low-cost PON. Optical source power is set to 0decibel-milliwatts (dBm) with data bit rate 1 Giga bit per second (tb = 1 ns).


Figure 6 shows the proposed architecture that incorporates a maximum of 𝐾 × 𝐾 transmitters, 𝑁 remote nodes, and 𝐾 × 𝐾 receiver modules. Here, 𝐾 and 𝐾 represent the number of spectral and temporal code word, whereas 𝑁 is the temporal code length. Each subscriber is assigned with a part of the transmitter and receiver module corresponding to a 2D vector permutation code word 𝐴 , . Furthermore, a hybrid ring and tree-based topology is adapted at the feeder and distribution level to facilitate deployment of the proposed architecture as a low-cost PON. Optical source power is set to 0 decibel-milliwatts (dBm) with data bit rate 1 Giga bit per second (tb = 1 ns).

ODN

RN1

RN K2

RN2

OCU

1RN2

OCU

2RN

2

CO

OLTTX

OLTRX

OCU

OCU

P2

P1

Decoder

-PIN1

PIN2C-Decoder

OS

OC

τ

τ

Temporal Decoder

Spectral Decoder

DFs

ONT

Figure 6. Proposed 2D PV-based OCDMA-Passive optical network architecture.

Figure 7 illustrates construction of the transmitter module in correspondence with the proposed 2D VP code word, 𝐴 , . For illustration purpose, an example of a single user 𝑈 , was considered, as shown in Table 3 with a 𝑋 and 𝑌 code words of [0 0 1 0 0 0 1 0] and [0 0 1 0 1 0 0 0] , respectively. In addition, Table 3 shows the allocation of respective wavelengths (𝜆 ) and time delays (𝜏 ) for corresponding chips in the spectral and temporal code sequences, respectively. For example, for user 𝑈 , , the spectral encoding was achieved by allowing the wavelengths centered at 𝜆 and 𝜆 , whereas the temporal encoding was achieved by employing 𝜏 and 𝜏 delay instants. Furthermore, for the user 𝑈 , under consideration, the transmitter modules incorporate a combination of broadband light sources (BBS), temporal and spectral encoders, erbium-doped fiber amplifier (EDFA), modulation, and switching arrangement.

OS

OC

τ

τ

Temporal Encoder

LED EDFA

OC

U

Data NRZ

MZM

DM

ux

OC

Spectral Encoder

Figure 7. Transmitter module.

Initially the broadband spectrum generated by the BBS, called light emitting diode (LED), is delivered to the temporal encoding arrangement, which contains a 1: 𝑤 optical splitter (𝑂𝑆 ). It can be observed from Table 3 that when ℎ = 0 in 𝐴 , , all the 𝑋 code words were delayed by the same instant. Therefore, employing a single time delay unit, in comparison with the conventional technique, can significantly reduce the complexity and cost of the system. 𝑂𝑆 splits the incoming signal into 𝑤 equal portions, which are then applied to the time delay units (TUs), as shown in Figure 6. The 𝑇𝑈 across each line for user 𝑈 , was proportional to the location of one chip of the time-spreading code word 𝑌 , respectively, as shown in Table 3. For example, in the placement of chips in the time-spreading codeword 𝑌 = 3,5 , suppose unit delay equals to τ, then the delay time of the 𝑇𝑈 for 𝑌 is (3𝜏, 5𝜏), respectively. End faces of both the 𝑇𝑈 were combined via 𝑤 : 1 optical combiner (𝑂𝐶 ) to complete the time-spreading encoding for the code words 𝐴 , , respectively.


Figure 7 illustrates construction of the transmitter module in correspondence with the proposed2D VP code word, Ag,h. For illustration purpose, an example of a single user U0,0 was considered, asshown in Table 3 with a Xth and Yth code words of [0 0 1 0 0 0 1 0] and [0 0 1 0 1 0 0 0], respectively.In addition, Table 3 shows the allocation of respective wavelengths (λs) and time delays (τs) forcorresponding chips in the spectral and temporal code sequences, respectively. For example, for userU0,0, the spectral encoding was achieved by allowing the wavelengths centered at λ3 and λ7, whereasthe temporal encoding was achieved by employing τ3 and τ5 delay instants. Furthermore, for theuser U0,0 under consideration, the transmitter modules incorporate a combination of broadband lightsources (BBS), temporal and spectral encoders, erbium-doped fiber amplifier (EDFA), modulation, andswitching arrangement.

Entropy 2020, 22, 576 11 of 19


Figure 6 shows the proposed architecture that incorporates a maximum of 𝐾 × 𝐾 transmitters, 𝑁 remote nodes, and 𝐾 × 𝐾 receiver modules. Here, 𝐾 and 𝐾 represent the number of spectral and temporal code word, whereas 𝑁 is the temporal code length. Each subscriber is assigned with a part of the transmitter and receiver module corresponding to a 2D vector permutation code word 𝐴 , . Furthermore, a hybrid ring and tree-based topology is adapted at the feeder and distribution level to facilitate deployment of the proposed architecture as a low-cost PON. Optical source power is set to 0 decibel-milliwatts (dBm) with data bit rate 1 Giga bit per second (tb = 1 ns).

ODN

RN1

RN K2

RN2

OCU

1RN2

OCU

2RN

2

CO

OLTTX

OLTRX

OCU

OCU

P2

P1

Decoder

-PIN1

PIN2C-Decoder

OS

OC

τ

τ

Temporal Decoder

Spectral Decoder

DFs

ONT


Figure 7 illustrates construction of the transmitter module in correspondence with the proposed 2D VP code word, 𝐴 , . For illustration purpose, an example of a single user 𝑈 , was considered, as shown in Table 3 with a 𝑋 and 𝑌 code words of [0 0 1 0 0 0 1 0] and [0 0 1 0 1 0 0 0] , respectively. In addition, Table 3 shows the allocation of respective wavelengths (𝜆 ) and time delays (𝜏 ) for corresponding chips in the spectral and temporal code sequences, respectively. For example, for user 𝑈 , , the spectral encoding was achieved by allowing the wavelengths centered at 𝜆 and 𝜆 , whereas the temporal encoding was achieved by employing 𝜏 and 𝜏 delay instants. Furthermore, for the user 𝑈 , under consideration, the transmitter modules incorporate a combination of broadband light sources (BBS), temporal and spectral encoders, erbium-doped fiber amplifier (EDFA), modulation, and switching arrangement.

OS

OC

τ

τ

Temporal Encoder

LED EDFA

OC

U

Data NRZ

MZM

DM

ux

OC

Spectral Encoder


Initially the broadband spectrum generated by the BBS, called light emitting diode (LED), is delivered to the temporal encoding arrangement, which contains a 1: 𝑤 optical splitter (𝑂𝑆 ). It can be observed from Table 3 that when ℎ = 0 in 𝐴 , , all the 𝑋 code words were delayed by the same instant. Therefore, employing a single time delay unit, in comparison with the conventional technique, can significantly reduce the complexity and cost of the system. 𝑂𝑆 splits the incoming signal into 𝑤 equal portions, which are then applied to the time delay units (TUs), as shown in Figure 6. The 𝑇𝑈 across each line for user 𝑈 , was proportional to the location of one chip of the time-spreading code word 𝑌 , respectively, as shown in Table 3. For example, in the placement of chips in the time-spreading codeword 𝑌 = 3,5 , suppose unit delay equals to τ, then the delay time of the 𝑇𝑈 for 𝑌 is (3𝜏, 5𝜏), respectively. End faces of both the 𝑇𝑈 were combined via 𝑤 : 1 optical combiner (𝑂𝐶 ) to complete the time-spreading encoding for the code words 𝐴 , , respectively.


Initially the broadband spectrum generated by the BBS, called light emitting diode (LED), isdelivered to the temporal encoding arrangement, which contains a 1 : w2 optical splitter (OSTX).It can be observed from Table 3 that when h = 0 in Ag,h, all the Xth code words were delayed by thesame instant. Therefore, employing a single time delay unit, in comparison with the conventionaltechnique, can significantly reduce the complexity and cost of the system. OSTX splits the incomingsignal into w2 equal portions, which are then applied to the time delay units (TUs), as shown inFigure 6. The TUTX across each line for user U0,0 was proportional to the location of one chip of thetime-spreading code word Yh, respectively, as shown in Table 3. For example, in the placement of chipsin the time-spreading codeword YT

1 = {3, 5}, suppose unit delay equals to τ, then the delay time ofthe TUTX for Y1 is (3τ, 5τ), respectively. End faces of both the TUTX were combined via w2 : 1 opticalcombiner (OCTX) to complete the time-spreading encoding for the code words Ag,0, respectively.

Table 3. Allocation of respective wavelengths (λs) and time delays (τs).


Table 3. Allocation of respective wavelengths (휆 ) and time delays (휏 ).

푨품,풉 흀ퟏ 흀ퟐ 흀ퟑ 흀ퟒ 흀ퟓ 흀ퟔ 흀ퟕ 흀ퟖ 흀ퟗ 흀ퟏퟎ 흀ퟏퟏ 흀ퟏퟐ 흀ퟏퟑ 흀ퟏퟒ 흀ퟏퟓ 흀ퟏퟔ 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0

흉ퟏ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟐ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟑ 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 흉ퟒ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟓ 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 흉ퟔ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟕ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟖ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟏ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟐ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟑ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟒ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟓ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟔ 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 흉ퟕ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 흉ퟖ 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0

Further, the output of the time-spreading encoder was delivered to an EDFA and 1: 푁 푂푆 , where 푁 corresponds to the number of users with reference to the spectral code words. EDFA was employed prior to the splitting arrangement in order to compensate the splitter losses and maintain the integrity of the time-spread optical pulses. For user 푈 , , the first port of the 1: 푁 푂푆 was delivered to the modulating arrangement where the Mach-Zhender modulator (MZM) modulates the incoming data bits with the optical signal by using an ON-OFF keying (OOK) format.

The modulated signal was delivered to the second stage of the encoding operation, namely, the spectral encoder, which was formed by the combination of 1: 푤 OS and 푤 : 1 multiplexer (MUX). Each leg of the 푀푈푋 : contained a bandpass filter that was tuned to allow the required spectrum with correspondence to the chip placement in 푋 code sequence, as shown in Table 3. Consequently, for user 푈 , , the spectral encoder allowed the spectrum located at 휆 and 휆 , respectively. Consequently, the 2D temporal and spectral encoding operation for the coder word 퐴 , of user 푈 , was achieved at the transmitter module.

Then, the end face of the spectral encoder was connected to a switching arrangement (SWA) via 푁 푁 : 1 optical coupler (푂퐶푈 ). The SWA was deployed to exploit the built-in redundancy of the ring topology and ensure desired connection availability at the feeder level. The SWA, as shown in Figure 6, contained a combination of 1: 2 푂퐶푈 and an optical switch, respectively, with port 1 as the input and ports 2 and 3 as the output ports, respectively. The 1: 2 푂퐶푈 received the encoded spectrum from 푁 푁 : 1 푂퐶푈 via input port 1. The encoded spectrum was equally forwarded towards the output ports 2 and 3, respectively. Port 2 of the 1: 2 푂퐶푈 extended towards the optical distribution network (ODN) that further connected with multiple remote nodes, whereas port 3 was fed to an optical switch 1: 2 푆푊 , as shown in Figure 6.

Under normal working conditions, port 2 of the 푆푊 is connected to an optical null and all traffic propagates in a clockwise direction towards the ODN, as shown in Figure 6 using red fiber. However, in a case of failure or cuts in the feeder fiber, Optical line terminator (OLT) unit directs the 푆푊 to change its position from port 2 to port 3, which provides a clockwise and counterclockwise flow traffic until the point of failure. Consequently, the proposed architecture can provide extended connection availability along with high spectral efficiency in comparison with the existing architecture.

Further, the output of the time-spreading encoder was delivered to an EDFA and 1 : NK1OSTX,where NK1 corresponds to the number of users with reference to the spectral code words. EDFA wasemployed prior to the splitting arrangement in order to compensate the splitter losses and maintainthe integrity of the time-spread optical pulses. For user U0,0, the first port of the 1 : NK1OSTX wasdelivered to the modulating arrangement where the Mach-Zhender modulator (MZM) modulates theincoming data bits with the optical signal by using an ON-OFF keying (OOK) format.

The modulated signal was delivered to the second stage of the encoding operation, namely, thespectral encoder, which was formed by the combination of 1 : w1 OS and w1 : 1 multiplexer (MUX).Each leg of the MUXw1:1 contained a bandpass filter that was tuned to allow the required spectrum with

Entropy 2020, 22, 576 12 of 19

correspondence to the chip placement in Xth code sequence, as shown in Table 3. Consequently, foruser U0,0, the spectral encoder allowed the spectrum located at λ3 and λ7, respectively. Consequently,the 2D temporal and spectral encoding operation for the coder word A0,0 of user U0,0 was achieved atthe transmitter module.

Then, the end face of the spectral encoder was connected to a switching arrangement (SWA) viaNK1NK2 : 1 optical coupler (OCUTX). The SWA was deployed to exploit the built-in redundancy of thering topology and ensure desired connection availability at the feeder level. The SWA, as shown inFigure 6, contained a combination of 1 : 2 OCUSWA and an optical switch, respectively, with port 1 asthe input and ports 2 and 3 as the output ports, respectively. The 1 : 2 OCUSWA received the encodedspectrum from NK1NK2 : 1 OCUTX via input port 1. The encoded spectrum was equally forwardedtowards the output ports 2 and 3, respectively. Port 2 of the 1 : 2 OCUSWA extended towards the opticaldistribution network (ODN) that further connected with multiple remote nodes, whereas port 3 wasfed to an optical switch 1 : 2 SWSWA, as shown in Figure 6.

Under normal working conditions, port 2 of the SWSWA is connected to an optical null and alltraffic propagates in a clockwise direction towards the ODN, as shown in Figure 6 using red fiber.However, in a case of failure or cuts in the feeder fiber, Optical line terminator (OLT) unit directs theSWSWA to change its position from port 2 to port 3, which provides a clockwise and counterclockwiseflow traffic until the point of failure. Consequently, the proposed architecture can provide extendedconnection availability along with high spectral efficiency in comparison with the existing architecture.

ODN essentially contains a combination of ring-based feeder fiber (FFR), remote nodes(RNK2

),

distribution fibers (DFN), and optical network terminals (ONTs). One end of the FFR relates to port 2of the OCUSWA in order to carry the traffic towards the ODN in a clockwise direction under a normalmode of operation, whereas, the other end terminated at port 3 of the SWSWA, as shown in Figure 6.FFR also contains multiple RNK2 to carry the traffic from feeder level to the respective ONTs at thedistribution level.

Each RNK2 consisted of two OCUs with the split ratio of 1 : 2(OCU1RN1

)and 1 : K1

(OCU2RN1

),

respectively. For user U0,0, RN1 was considered, as shown in Figure 6. The OCU1RN1 received the FFR

through its input port 1 and split the incoming signal into two equal portions. One portion (via port 2of the OCU1RN1 ) of the incoming signal was sent towards the OCU2RN1 , whereas another portion (viaport 3 of the OCU1RN1 ) was forwarded towards the RN2 (Figure 6).

The spectral/temporal multiplexed signal was received from port 2 of the OCU1RN1 via the inputport of the OPCU2RN1 . The second optical coupler at RNN had a split of 1 : K1, which was used tocarry the encoded spectrum towards the concerned ONTs via their respective DFs.

Port 3 of the OCU1RN1 further extended the ring-based fiber and was connected to the RN2,which consisted of the similar arrangement as discussed earlier. Since the number of OCU1RNs usedthroughout the network to support the given number of users was dependent of the value of Yth codesequences, it was of prime importance to keep the number of codes as few as possible to address thepower constraints of the ring-based topology.

The ONT module for the proposed 2D architecture employed a time-based decoding arrangement,which was designed in accordance with the temporal encoder. It split the incoming signal into twoequal portions while using a 1 : 2 OSTD. Each leg of the OSTD was connected to a TU that wascalculated as (S− 1− j), where j is the chip position in the YT

0 code sequence for user U0,0. Outputsfrom the TUs were combined with the help of a 1 : 2 OCTD and forwarded for spectral decoding.

The spectral decoder essentially contained a balanced decoding arrangement commonly referredto as complementary subtraction detection schemes (CSD). CSD for the proposed architecture consistedof a 1:2 OSONT that split the time decoded-signal into two equal portions. One portion was fed to afilter arrangement in the upper leg of the CSD decoder, whereas another portion was fed to anotherfilter arrangement at the lower leg of the decoder, as shown in Figure 6. Filters in the upper leg ofthe CSD decoder contained a combination of fiber Bragg-grating (FBG) filters that were centered inaccordance with the X1 code spectral signature.

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The lower leg of the CSD decoder employed a combination of FBG filters configured to complementto the 1s in the X1 code sequence. In other words, the lower leg of the CSD decoder for user U0,0

extracted the spectrum that was in complement with the X1 code sequence. Then, resulting signalsfrom both legs of the spectral decoder related to respective PIN photodiodes in order to convert thesignal from optical to electrical domain for necessary processing. The output from the PIN photodiodeswas further connected to the subtractor arrangement that subtracted the output from both legs ofthe CSD decoder to recover the intended spectrum with maximum power units for the intendedsubscribers and 0 power units for interfering users.

6. Proof of Concept

This section analyzes the performance of the proposed setup through system implementationin an optical networks simulation software called Optisystem. The proposed system architecturepresented in Figures 6 and 7 was utilized to implement the simulation model for eight subscribersaccessing the medium simultaneously. To deploy eight subscribers across the network, four spectralcoding schemes and two temporal schemes were utilized. Consequently, the simulation model wasimplemented with K1 = 4, K2 = 2 at g = 0, 1, 2, 3 and h = 0, 1.

The OLT module was implemented in accordance with Figure 7, which shows a transmittermodule configured at g = 0, 1, 2, . . . , K1 − 1 and h = 0. As mentioned earlier, for h = 0 in Ag,h, allthe spectral code sequences could be delayed by the same instant. Therefore, two LEDs followedby two temporal decoders were employed to configure encoding arrangements for eight subscribersaccessing the medium simultaneously. Now, for h = 0, four subscribers were configured with a singlebroad-spectrum LED that related to time delay units through a 1:2 optical splitter having 0 dB loss.Both legs of the optical splitter were fed into time delay units that were configured in accordance withthe position of 1s in the YT

0 coding scheme. For instance, the TU connected with the top leg of thesplitter was delayed by an amount of 3

Bit rate∗8 , whereas the bottom TU was configured with the delayof 5

Bit rate∗8 , respectively. Similarly for h = 1, the TUs were configured with the delays of 6Bit rate∗8 and

8Bit rate∗8 in accordance with the position of 1s at the YT

1 coding scheme.The end face of the TUs were connected to a 2:1 optical combiner with 0 dB loss, followed by an

EDFA module. Specification of the system components used during simulation analysis are givenas Table 4. The amplified time-delayed signal from EDFA module related to a 1:4 optical coupler,in accordance with K1 = 4. Each output leg of the coupler was fed into an individual MZM inorder to modulate the signal with the user’s information. After modulation, the process of spectralencoding was initiated by employing a combination of 1:2 optical splitter and MUX arrangement.MUX arrangement for each subscriber was configured to reflect the frequency bins in accordance withposition of 1s in the Xg code sequence. Then, for user U0,0, the spectral encoder allowed the spectrumlocated at λ3 and λ7, respectively. Similarly, for user U0,1, a spectral encoding arrangement with samefilter configuration was used to allow the spectrum located at λ3 and λ7, respectively. Consequently,the 2D temporal and spectral encoding operation for the coder word A0,0 till A3,1 was achieved at thetransmitter module.

Outputs from the spectral encoders were connected to an 8:1 optical coupler followed by 1:2coupler having 0 dB loss and were configured in accordance with Figure 6. Moreover, two remotenodes were employed in the simulation model, in accordance with K2 = 2. The ONT module for thesimulation arrangement was configured accordingly to recover and detect the intended spectrum, inaccordance with the proposed coding scheme. Each ONT module started with a 1:2 optical splitter toinitiate the process of temporal decoding. Each leg of the splitter was fed to a TU with delays calculatedthrough (S− 1− j). The end face of each TU related to a 2:1 optical combiner to conclude the process oftemporal decoding.

This process was followed by spectral decoding that was implemented with the help of balanceddetectors. Balanced detectors split the incoming signal into two parts. One part was applied to anarrangement of FBG filters that were configured in accordance with spectral signature of the encoder.

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For example, for user U0,0, FBG filters at the top leg were configured to recover λ3 and λ7, whereas theFBG filter employed at the bottom leg was used to recover the complement of the intended signature.The output of both filter arrangements was passed through PIN photodiodes and subtracted to recoverthe intended spectrum with maximum auto- and minimum cross-correlation.

Table 4. Parameters used in simulation analysis.

System Component Value

LED spectrum 30 nmLED frequency 1490 nm

EDFA Gain 9 dBEncoder bandwidth 0.4 nm

MZM extinction ratio 30 dBSMF attenuation 0.25 dB/kmSMF dispersion 18 ps/nm/kmFF ring length 20 Km

DF length 5 KmDecoder bandwidth 0.4 nmPIN responsitivity 0.75 A/WPIN dark current 10 nA

PIN thermal noise 1e−22 W/Hz

Then, for the initial analysis, the performance of the proposed system was analyzed in terms ofdata rate versus bit error rate. Moreover, with an EDFA of 9 dB gain, power at the ONTs of the firstremote node RN1 was set at 0 dBm, respectively. Figure 8 shows the eye diagrams and BER of theproposed setup at 1 Gbps and 2 Gbps of data for randomly selected nodes of ONTRN1 . It was observedthat the proposed setup was well able to support high data rates of up to 2 Gbps. Moreover, analysisof the BER and eye diagrams validated the implementation setup such that BER increased with anincrease in the amount of data transmitted between the OLT and ONTs’ modules.


Then, for the initial analysis, the performance of the proposed system was analyzed in terms of data rate versus bit error rate. Moreover, with an EDFA of 9 dB gain, power at the ONTs of the first remote node 𝑅𝑁 was set at 0 dBm, respectively. Figure 8 shows the eye diagrams and BER of the proposed setup at 1 Gbps and 2 Gbps of data for randomly selected nodes of 𝑂𝑁𝑇 . It was observed that the proposed setup was well able to support high data rates of up to 2 Gbps. Moreover, analysis of the BER and eye diagrams validated the implementation setup such that BER increased with an increase in the amount of data transmitted between the OLT and ONTs’ modules.

This can be attributed to the fact that pulse width decreased with an increase in the data bits, which made the system more vulnerable to distortion across the medium. Consequently, a higher data rate will yield a higher BER. However, analysis showed that for an agreeable BER of 10 the proposed setup was able to provide the desired performance up to 2 Gbps of data, owing to the efficient cross-correlation properties at the 𝑋 code sequence and proficient design of the proposed setup that maintained a nominal signal power to yield a desired signal-to-noise ratio and, hence, BER.

(a)

Figure 8. Cont.


(b)

Figure 8. Eye diagrams for downlink traffic at (a) 1 Gbps and (b) 2 Gbps.

To further analyze the impact of the power budget on the overall performance of the setup, analysis was made at 1 Gbps of data by randomly selecting nodes at each remote node from 𝑅𝑁 −𝑅𝑁 . Moreover, through the application of nine EDFA at the transmitter module, 0 dBm, −3 dBm, and −6 dBm power was observed at the 𝑂𝑁𝑇 , 𝑂𝑁𝑇 , and 𝑂𝑁𝑇 , respectively. Eye diagrams and BER analysis in Figure 9 show that the proposed setup was capable enough to handle the power drops at each remote node and provide desired results for an acceptable BER of 10 . Results’ analysis also validated the proposed model, which showed a relevant decrease in the BER along with a decrease in the power each ONT of alternated remote nodes.

(a)


This can be attributed to the fact that pulse width decreased with an increase in the data bits,which made the system more vulnerable to distortion across the medium. Consequently, a higherdata rate will yield a higher BER. However, analysis showed that for an agreeable BER of 10−9 theproposed setup was able to provide the desired performance up to 2 Gbps of data, owing to the efficientcross-correlation properties at the Xth code sequence and proficient design of the proposed setup thatmaintained a nominal signal power to yield a desired signal-to-noise ratio and, hence, BER.

To further analyze the impact of the power budget on the overall performance of the setup,analysis was made at 1 Gbps of data by randomly selecting nodes at each remote node from RN1 −RN3.Moreover, through the application of nine EDFA at the transmitter module, 0 dBm, −3 dBm, and−6 dBm power was observed at the ONTRN1 , ONTRN2 , and ONTRN2 , respectively. Eye diagrams andBER analysis in Figure 9 show that the proposed setup was capable enough to handle the power dropsat each remote node and provide desired results for an acceptable BER of 10−9. Results’ analysis alsovalidated the proposed model, which showed a relevant decrease in the BER along with a decrease inthe power each ONT of alternated remote nodes.


(b)


To further analyze the impact of the power budget on the overall performance of the setup, analysis was made at 1 Gbps of data by randomly selecting nodes at each remote node from 𝑅𝑁 −𝑅𝑁 . Moreover, through the application of nine EDFA at the transmitter module, 0 dBm, −3 dBm, and −6 dBm power was observed at the 𝑂𝑁𝑇 , 𝑂𝑁𝑇 , and 𝑂𝑁𝑇 , respectively. Eye diagrams and BER analysis in Figure 9 show that the proposed setup was capable enough to handle the power drops at each remote node and provide desired results for an acceptable BER of 10 . Results’ analysis also validated the proposed model, which showed a relevant decrease in the BER along with a decrease in the power each ONT of alternated remote nodes.

(a)

Figure 9. Cont.


(b)

(c)

Figure 9. Eye diagrams for downlink traffic at (a) −6 dBm, (b) −3 dBm, and (c) 0 dBm.

In order to analyze the impact of the switching arrangement and observe the capability of the proposed setup to handle traffic in both clockwise and counterclockwise directions, the proposed model was simulated with an optical switch after the transmitter module. Moreover, for fair analysis, the number of simultaneous users accessing the medium was reduced to 𝐾 = 4, 𝐾 = 2 with 𝑁 = 8. Analysis was performed at 1 Gbps of data and port 2 of the switch was initially engaged to observe the flow of traffic in a clockwise direction. In the second phase of the simulation, port 3 was engaged to analyze the flow of traffic in a counterclockwise direction to mimic a state of failure.

Figure 9. Eye diagrams for downlink traffic at (a) −6 dBm, (b) −3 dBm, and (c) 0 dBm.

In order to analyze the impact of the switching arrangement and observe the capability of theproposed setup to handle traffic in both clockwise and counterclockwise directions, the proposedmodel was simulated with an optical switch after the transmitter module. Moreover, for fair analysis,the number of simultaneous users accessing the medium was reduced to K1 = 4, K2 = 2 with N2 = 8.Analysis was performed at 1 Gbps of data and port 2 of the switch was initially engaged to observe theflow of traffic in a clockwise direction. In the second phase of the simulation, port 3 was engaged toanalyze the flow of traffic in a counterclockwise direction to mimic a state of failure.

Figure 10 shows the eye diagrams and BER analysis for the flow of traffic in both clockwise andcounterclockwise directions. It is evident that the proposed setup was able to support the flow oftraffic in both directions with minuscule effect on the overall performance. It can be observed that for1 Gbps of data almost the same BER was obtained at the randomly selected ONT of RN1 (clockwiseflow of traffic) and RN2 (counterclockwise flow of traffic). Hence, the proposed VP-based 2D OCDMAsystem was not only able to provide high capacity in terms of data, reach, and the number of users, butwas also capable of providing relative support against feeder fiber failure, which is novel, as comparedto the existing 2D OCDMA architecture.

Entropy 2020, 22, 576 17 of 19


Figure 10 shows the eye diagrams and BER analysis for the flow of traffic in both clockwise and counterclockwise directions. It is evident that the proposed setup was able to support the flow of traffic in both directions with minuscule effect on the overall performance. It can be observed that for 1 Gbps of data almost the same BER was obtained at the randomly selected ONT of 𝑅𝑁 (clockwise flow of traffic) and 𝑅𝑁 (counterclockwise flow of traffic). Hence, the proposed VP-based 2D OCDMA system was not only able to provide high capacity in terms of data, reach, and the number of users, but was also capable of providing relative support against feeder fiber failure, which is novel, as compared to the existing 2D OCDMA architecture.

(a)

(b)

Figure 10. Eye diagrams for downlink traffic at (a) clockwise and (b) counterclockwise directions. Figure 10. Eye diagrams for downlink traffic at (a) clockwise and (b) counterclockwise directions.

The 2D PV code performance, in terms of BER and number of supportable clients, is shown inFigure 11. As the number of users increased the quality of the received signal deteriorated due tothe occurrence of MAI among them. Thus, system signal to noise ratio (SNR) and BER degraded.Moreover, BER values of 2D PV code (K1 = 62, K2 = 3; where K1 and K2 refers to number of subscribersin spectral and spatial domain) were compared with existing techniques: Diluted perfect differencecode (M = 63, P = 3) and diagonal eigenvalue unity code (M = 63, P = 3; M and P represents number ofsubscribers in spectral and spatial domain). It was observed that supported clients were 20, 40, and 110for 2D diluted perfect difference (DPD), 2D diagonal eigen value (DEU), and 2D PV code, respectively,at the minimum acceptable BER value of 10−9. In particular, multi diagonal (MD) code (M = 63, P = 3)is also plotted and results indicate an overlap with our proposed code due to their similar properties.

Entropy 2020, 22, 576 18 of 19


The 2D PV code performance, in terms of BER and number of supportable clients, is shown in Figure 11. As the number of users increased the quality of the received signal deteriorated due to the occurrence of MAI among them. Thus, system signal to noise ratio (SNR) and BER degraded. Moreover, BER values of 2D PV code (K1 = 62, K2 = 3; where K1 and K2 refers to number of subscribers in spectral and spatial domain) were compared with existing techniques: Diluted perfect difference code (M = 63, P = 3) and diagonal eigenvalue unity code (M = 63, P = 3; M and P represents number of subscribers in spectral and spatial domain). It was observed that supported clients were 20, 40, and 110 for 2D diluted perfect difference (DPD), 2D diagonal eigen value (DEU), and 2D PV code, respectively, at the minimum acceptable BER value of 10−9. In particular, multi diagonal (MD) code (M = 63, P = 3) is also plotted and results indicate an overlap with our proposed code due to their similar properties.

Figure 11. Bit error rate vs. number of active users for 2D PV (K1 = 63, K2 = 3), 2D diagonal eigen value unity code (M = 63, P=3), 2D diluted perfect difference code (M = 63, P =3), and 2D Multi Diagonal code (K1 = 62, K2 = 3) with 0 dBm effective transmitted power at data rate 622 Mbit/sec.

7. Conclusions

A new 2D PV coding scheme was proposed based on a WHTS coding approach and possesses several advantages over the existing families, such as simplicity of code construction, no limitation of the selection of any positive integer weight, and high degree of cardinality with increased flexibility. The proposed code can be employed for both synchronous and asynchronous incoherent OCDMA environment. Results indicated that 2D W-T PV code had improved system performance due to reduced error probability with MAI and phase induced intensity noise (PIIN) effects suppression and easier code implementation capabilities. For future implementations, simple direct detection method can be employed in the receiver design, which is cost effective and less complex due to the utilization of single-photo diode and low-pass filter circuit. The numerical results indicated that the 2D PV code provided better performance in terms of system parameters such as transmitted power at the source, cardinality, BER, and data rate. The simulation results demonstrated successful implementation of the 2D PV-based OCDMA scheme and make it applicable for all optical networks in practice by maintaining optimal BER (10−9) required for error-free transmission at minimum data rate.

Figure 11. Bit error rate vs. number of active users for 2D PV (K1 = 63, K2 = 3), 2D diagonal eigenvalue unity code (M = 63, P = 3), 2D diluted perfect difference code (M = 63, P = 3), and 2D MultiDiagonal code (K1 = 62, K2 = 3) with 0 dBm effective transmitted power at data rate 622 Mbit/sec.

7. Conclusions

A new 2D PV coding scheme was proposed based on a WHTS coding approach and possessesseveral advantages over the existing families, such as simplicity of code construction, no limitation ofthe selection of any positive integer weight, and high degree of cardinality with increased flexibility.The proposed code can be employed for both synchronous and asynchronous incoherent OCDMAenvironment. Results indicated that 2D W-T PV code had improved system performance due toreduced error probability with MAI and phase induced intensity noise (PIIN) effects suppressionand easier code implementation capabilities. For future implementations, simple direct detectionmethod can be employed in the receiver design, which is cost effective and less complex due to theutilization of single-photo diode and low-pass filter circuit. The numerical results indicated that the 2DPV code provided better performance in terms of system parameters such as transmitted power at thesource, cardinality, BER, and data rate. The simulation results demonstrated successful implementationof the 2D PV-based OCDMA scheme and make it applicable for all optical networks in practice bymaintaining optimal BER (10−9) required for error-free transmission at minimum data rate.

Author Contributions: H.Y.A., M.Z. and W.A.I. designed the research. H.Y.A. and M.Z. performed the codeprogramming. W.A.I. carried out simulation analysis. T.S., H.Y.A. and A.C. performed the analysis of the resultsand the results’ interpretation. T.S., H.Y.A. and W.A.I. wrote the first draft together, supported by T.S., A.C. andP.F. commented on the draft and all authors finalized it. T.S. and A.C. were corresponding authors. All authorshave read and agreed to the published version of the manuscript.

Funding: This research received no external funding.

Conflicts of Interest: The authors declare no conflict of interest.

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Documents

Two-Dimensional Permutation Vectors’ (PV) Code for Optical